dz=(cosy+xsiny)’e^x+(cosy+xsiny)(e^x)’
=(-sinydy+sinydx+xcosydy)e^x+(cosy+xsiny)e^xdx
=e^x(siny+xsiny+cosy)dx+e^x(xcosy-siny)dy
dz/dx= e^x(siny+xsiny+cosy)
dz/dy= e^x(xcosy-siny)
所以:
d^2z/dx^2=e^x(siny+xsiny+cosy)+e^xsiny
=e^x(2siny+xsiny+cosy).
d^2z/dy^2=e^x(-xsiny-cosy)=-e^x(xsiny+cosy).